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On the Structure of Graphic DLI-Sets

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Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

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Abstract

The DLI-sets were defined in connection with the problem of deciding the context-freeness of the languages Q n = Q ∩ (ab *)n} [14]. It is conjectured in [3] that Q n is context-free for all positive numbers n. This conjecture was verified for the cases where \( n = p_1^{f_1 } ... p_k^{f_k } \) with distinct prime numbers p 1,...,p k for which

$$ \sum\limits_{i = 1}^k {{1 \mathord{\left/ {\vphantom {1 {p_i < {4 \mathord{\left/ {\vphantom {4 5}} \right. \kern-\nulldelimiterspace} 5}}}} \right. \kern-\nulldelimiterspace} {p_i < {4 \mathord{\left/ {\vphantom {4 5}} \right. \kern-\nulldelimiterspace} 5}}}} $$
(1)

. (1) holds. (See.: [18]). To find a proof for the general case it would be useful to find special DLI sets other then the boxes used in the proof of the former result. In this paper a sufficient condition is given for DLI sets to be stratified semilinear

This research was supported by the Hungarian-German scientific- technological research project No D 39/2000 in the scope of the treaty contracted by the Hungarian Ministry of Education and his German contractual partner BMBF.

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Authors and Affiliations

  1. Department of Mathematics, Berzsenyi College, H-9700, Szombathely, Hungary

    László Kászonyi

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  1. László Kászonyi
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Editors and Affiliations

  1. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

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Kászonyi, L. (2003). On the Structure of Graphic DLI-Sets. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_31

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  • DOI: https://doi.org/10.1007/3-540-45005-X_31

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  • Print ISBN: 978-3-540-40431-6

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